Reconstruction of two-valued matrices from their two projections

J. H.B. Kemperman, A. Kuba

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A matrix is said to be two-valued if its elements assume at most two different values. We studied the problem of reconstructing a two-valued matrix from its marginals-that is, from its row sums and column sums-but without any knowledge of the value pair on hand. Provided at least one of these marginals is nonconstant, only finitely many (though possibly many) value pairs can lead to a valid reconstruction. Our considerations lead to an efficient algorithm for calculating all possible solutions, each with its own value pair. Special attention is given to uniqueness pairs-that is, value pairs to which there corresponds precisely one matrix having the correct marginals. Unless both marginals are constant, there can be no more than two uniqueness pairs.

Original languageEnglish
Pages (from-to)110-117
Number of pages8
JournalInternational Journal of Imaging Systems and Technology
Volume9
Issue number2-3
DOIs
Publication statusPublished - 1998

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Software
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering

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